Problem: A horse 24 feet from the center of a merry-go-round makes 32 revolutions. In order to travel the same distance, how many revolutions would a horse 8 feet from the center have to make?
The radius of the circular path of the horse closer to the center is $\frac{1}{3}$ of the radius of the path of the horse farther from the center.  Since circumference is directly proportional to radius, the length of shorter path is $\frac{1}{3}$ of the length of the longer path.  Therefore, 3 times as many revolutions must be made to go the same distance, which is $32\times3=\boxed{96}$ revolutions.